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289 LearnersLast updated on November 18, 2025
Profit and Loss
Have you ever wondered how the shopkeepers decide the price of toys? That is where the concept of profit and loss comes in. Profit and loss statements show how much we gain or lose when we sell something. In this article, we will learn about profit and loss, their formula, and how to calculate them.
What is Profit and Loss?
Profit and loss are terms commonly used by entrepreneurs, shopkeepers, and retailers to understand whether a product or business is earning money or facing a loss.
A profit occurs when the selling price of a product exceeds its cost price, whereas a loss occurs when the cost price exceeds the selling price. For example, when shopping online for the same product from two different stores. If you buy from the store offering a lower price, the amount you save is the profit.
To better understand the concept, let’s explore some basic ideas about profit and loss. They are:
- Profit (P): Profit is the amount gained when a product is sold for more than its cost price
- Loss (L): Loss is the amount lost when a product is sold for less than its cost price
- Cost Price (CP): The cost price is the amount paid to purchase a product or commodity. There are two types of CP:
- Selling Price (SP): Selling price is the amount for which a product is sold. It is also known as the sale price.
- Market Price (MP): The price set by shopkeepers is usually higher to offer customers discounts.
Profit and Loss Formula
The profit and loss formula helps us to calculate how much is gained or lost in a transaction. These formulas are based on the CP and SP of a product.
Profit Formula
The profit formula helps us determine the profit earned when a product is sold for more than its cost price. A business makes a profit when the selling price exceeds the cost price. So, the profit is the difference between the selling price and the cost price. The formula is:
\(Profit = SP - CP \)
Loss Formula
To calculate the amount lost when the selling price is lower than the cost price, we use the loss formula. A business is at a loss when the selling price is less than the cost price. So, loss is the difference between the cost price and the selling price. The formula is:
\(Loss = CP - SP \)
Discount Formula
A discount is the amount by which the marked price is reduced. The discounts amount can be calculated using the formula:
\(Discount = MP - SP \)
Where MP is the marked price and SP is the selling price.
Profit and Loss Percentage
Profit and loss percentages help us understand how much profit or loss a product generates as a percentage. These values are calculated using formulas based on the cost price and selling price. For better understanding, let's learn some formulas for calculating profit percentage, loss percentage, discount, and markup.
Profit Percentage (%)
Profit percentage is the profit amount earned on a product compared to its cost price. The profit percentage is calculated using the formula:
\( \text{Profit %} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \)
Loss percentage (%)
The loss percentage is the loss incurred relative to the original cost. The loss percentage formula is:
\( \text{Loss %} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \)
Discount Percentage
Discount percentage is the reduction in a product's price from its marked price. The formula is:
\(\text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 \)
Where MP is the marked price
Markup Percentage:
The markup percentage is used to find how much a seller increases the CP to set the SP. The formula to find the markup percentage is:
\(\text{Markup Percentage} = \left( \frac{\text{Markup}}{\text{Cost Price}} \right) \times 100 \)
Tips and Tricks to Calculate Profit and Loss
Students sometimes get confused when calculating profit and loss. In this section, we’ll focus on a few tips and tricks to save time and make our lives easier.
- Memorize the basic formulas like:
\(Profit = SP - CP \)
\(Loss = CP - SP \)
\({\text {Profit %}} = {{\text {profit}} \over CP} × 100 \)
\({\text {Loss % }}= ({\text {loss}} / CP) × 100\)
- To help children understand the concepts of profit and loss, parents should let them observe price tags, discounts, and bills.
- When finding the profit and students, students should write each step clearly, like identifying CP, SP, profit or loss, and then the percentage.
- Teachers can use educational apps, digital worksheets, or interactive quizzes to help students understand the concept.
- Students can draw a profit-loss table to identify CP, SP, profit, and loss.
Common Mistakes and How to Avoid Them in Profit and Loss
Students are prone to make mistakes when dealing with any mathematical calculations, and profit and loss is not an exception. So, to avoid such mistakes, let us learn about a few common mistakes made while calculating profit and loss.
Mistake 1
Confusion Between Cost Price and Selling Price
Remember that cost price (CP) is what we pay for a product and selling price (SP) is how much we sell it for.
For example, if we buy a pencil for $1 and sell the same pencil for $2, then the CP is $1 and the SP is $2.
Mistake 2
Using the Wrong Formula
While memorizing and using the formulas for profit and loss, it is easy to mix up the values.
For example, when calculating the profit, students might incorrectly write the formula as P = CP - SP. Whereas, the correct formula is P = SP - CP.
Mistake 3
Calculation Errors
Even after using the correct formula, there is a possibility that the final answer may not be correct. This happens if we make mistakes while multiplying or dividing. Double check all the steps to make sure the calculations are correct.
Mistake 4
Ignoring Units
Sometimes, students tend to ignore the units such as dollars or pounds while writing the answers. Always remember to mention the currency while calculating profit and loss.
Mistake 5
Misreading the Question
Always read and understand the question before calculating. For example, solving for loss when the question asks for loss percentage will result in an error.
Real-World Applications of Profit and Loss
Profit and loss tell us if we are making money or losing it. Shops, restaurants, and online sellers use them to make wise choices and plan better. Here are a few applications of profit and loss.
- Retail Businesses: Shops calculate profit and loss on each product to determine overall business performance.
- Stock Market Investments: Investors track gains and losses on stocks to decide when to buy or sell.
- E-commerce Platforms: Online sellers use profit and loss calculations to price products competitively while ensuring profitability.
- Manufacturing: Companies assess profit and loss on products after factoring in raw materials, labor, and overhead costs.
- Restaurants & Cafés: Profit and loss is tracked on food items and menu sales to manage costs and pricing strategies.
Solved Examples for Profit and Loss
Problem 1
A toy costs $40, and it is sold for $60. Find the profit.
$20.
Explanation
To find the profit, we use the formula, \(P = SP - CP\)
Substituting the values, we get, \(P = 60 - 40 = 20\)
Therefore, the profit is $20.
Problem 2
A book was bought for $80 but sold for $65. Find the loss.
$15.
Explanation
The formula to find loss is, \(L = CP - SP\)
Substituting the values, we get, \(L = 80 - 65 = 15\)
Hence, the loss is $15.
Problem 3
A pen costs $10 and is sold for $20. Find the profit percentage.
100%.
Explanation
To find the profit percentage, let us first find the profit.
So, \(P = SP - CP\)
Substituting the values, we get, \(P = 20 - 10 = 10\).
Now, the profit percentage can be found by using the formula,
\({\text {Profit %}} = {{\text {profit}} \over CP} × 100 \)
Here, \(P\% = {10 \over 10} × 100 = 100\)
Therefore, the profit percentage is 100%.
Problem 4
A laptop is sold for $8,000 at a 20% loss. Find the cost price.
$10000.
Explanation
Here, the selling price (SP) is $8000 and the lost percentage is 20%. Now, to find the cost price (CP), we can use the formula,
\(CP = \frac{SP}{1 - \frac{\text{Loss %}}{100}} \)
Substituting the values, we get, \(CP = \frac{8000}{1 - \frac{\text{20}}{100}} \)
\(CP = \frac{8000}{(1 - 0.2)} \)
\(= \frac{8000}{0.8} \)
= 10000
Therefore, the cost price of the laptop is $10,000.
Problem 5
A table costs $2,000. The shopkeeper is selling it at a 20% loss. What is the selling price?
$1600.
Explanation
Here, we need to first calculate the loss amount. For that, we use the formula,
\({\text {Loss amount}} = CP × {{\text {Loss percentage }}\over 100}\)
Substituting the values, we get, loss amount \(= 2000 × {20\over 100}\)
Therefore, loss amount \(= 2000 × 0.2 = 400\)
Now that we know the loss amount, we can find the selling price by using the formula,
\( SP = CP - {\text {Loss Amount}}\)
Substituting the values, \(SP = 2000 - 400 = 1600\)
Therefore, the selling price is $1600.
FAQs on Profit and Loss
1.How to analyze profit and loss?
2.What is a balance sheet?
3.How to calculate net income?
4.What is the full form of Ebitda?
5.What is the full form of PAT?
6.What is profit and loss management?
7. What are the two types of profit and loss?
Dr. Sarita Ghanshyam Tiwari
About the Author
Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo
Fun Fact
: She believes math is like music—once you understand the rhythm, everything just flows!
